A330488 Primes p such that p+2 is prime and p+A001414(p+1)+(p+2) is prime.

5, 11, 107, 419, 431, 461, 1019, 1289, 1301, 1427, 1481, 2087, 3119, 3467, 3539, 4091, 4241, 5279, 5651, 5849, 5867, 6689, 7331, 8819, 9419, 9461, 9929, 10037, 10091, 11117, 11831, 11939, 14627, 16139, 16361, 17207, 17387, 17681, 18041, 18311, 20639, 20771, 22277, 22961, 23027, 23201, 25847

Offset: 1

Author

J. M. Bergot and Robert Israel, Dec 16 2019

Keywords

• nonn

Comments

If q, 18*q-1, 18*q+1 and 37*q+8 are prime, then 18*q-1 is in the sequence. Dickson's conjecture implies that there are infinitely many such q, and thus that this sequence is infinite.

Examples

			a(3) = 107 is in the sequence because 107 and 109 are primes, A001414(108) = 2*2+3*3 = 13, and 107+13+109 = 229 is prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001414. Subsequence of A001359.

Programs

Maple

filter:= proc(p) isprime(p) and isprime(p+2) and isprime(2*p+2+add(s[1]*s[2],s=ifactors(p+1)[2]))  end proc:select(filter, [seq(i,i=5..10^5,6)]);

PARI

\\ using A001414(n) written by M. F. Hasler
A001414(n)=(n=factor(n))[,1]~*n[,2];
forprime(p=3,26000,my(pp1=p+1);if(isprime(p+2),if(isprime(A001414(pp1)+2*pp1),print1(p,", ")))) \\ Hugo Pfoertner, Dec 17 2019